A simple strategy for constitutive modelling of timber Hamid Valipour a,⇑ , Nima Khorsandnia a , Keith Crews b , S. Foster a a Centre for Infrastructure Engineering and Safety (CIES), School of Civil and Environmental Engineering, The University of New South Wales (UNSW), Sydney, Australia b Centre for Built Infrastructure Research (CBIR), School of Civil and Environmental Engineering, University of Technology (UTS), Sydney, Australia highlights  Development of an orthotropic constitutive law for timber.  Nonlinear finite element analysis of timber and engineered wood products.  Capturing failure mode of timber using isotropic material models.  Application of theory of composites for modelling timber behaviour. article info Article history: Received 1 April 2013 Received in revised form 23 November 2013 Accepted 26 November 2013 Available online 18 December 2013 Keywords: Composite Damage model Nonlinear finite element Failure envelop abstract This paper focuses on development of a simple technique for modelling anisotropic behaviour of timber and engineered wood products. In the proposed approach, timber is treated as a composite material comprising a matrix with smeared fictitious reinforcing fibres in the principal directions. The matrix is assumed to be isotropic with a piecewise continuous failure envelop in the bi-axial stress space and the reinforcements follow uni-axial stress–strain relationships with different strengths under tension and compression. The stress–strain relationship of timber is obtained by superimposing the constitutive law of matrix and the fictitious reinforcements based on the principles of compatibility and equilibrium. Such a modelling strategy provides a simple platform for calibration of the constitutive law against avail- able mechanical properties of the timber in different directions (i.e. parallel or perpendicular to the grain). The proposed modelling technique is implemented in a finite element code and the developed analytical tool is verified by examples taken from the literature including bending tests on timber beams with notches and web openings, embedding tests on timber and push-out tests on TCC joints. It is shown that the proposed modelling strategy can adequately capture the mode of failure as well as the nonlinear behaviour of timber at local and global level. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction In the last decade, timber and timber–concrete composite (TCC) structures have found extensive structural applications because of the lower cost of construction and maintenance, as well as better sustainability compared with reinforced concrete and steel. In par- ticular the new engineered wood products (i.e. laminated veneer lumber (LVL), glued-laminated timber (glulam), cross-laminated timber (CLT) and oriented strand boards (OSB)) with improved structural characteristics have made it possible for structural engi- neers to design and construct large buildings that are as robust as steel and reinforced concrete but more sustainable. Accordingly, there is a need for development of simple yet accurate modelling strategies that can adequately capture the failure modes and load–deflection response of timber and engineered wood products. Sawn and engineered timber such as LVL, glulam, CLT and OSB are anisotropic (orthotropic or two-dimensionally isotropic) mate- rials with different strengths in tension and compression [1]. Also, behaviour of timber is strongly direction-dependent with large ra- tios of mechanical properties such as modulus of elasticity or strength between the respective values parallel and perpendicular to the grain directions. In tension, timber exhibits a nearly linear elastic–brittle failure behaviour and under compression the hard- ening part of the stress–strain diagram is nonlinear with limited ductility up to ultimate stress which is followed by a mild soften- ing part [2,3]. In addition, compression perpendicular to the grain direction can lead to wood densification and subsequent increase of yield (ultimate) strength. Apart from anisotropy, wood is an inhomogeneous material ow- ing to presence of knots and defects. These defects/imperfections can locally affect the grain deviation and subsequently influence 0950-0618/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2013.11.100 ⇑ Corresponding author. Address: School of Civil and Environmental Engineering, The University of New South Wales, Sydney, Kensington, NSW 2052, Australia. Tel.: +61 2 9385 6191. E-mail address: H.Valipour@unsw.edu.au (H. Valipour). Construction and Building Materials 53 (2014) 138–148 Contents lists available at ScienceDirect Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat